It's been fairly well explained now. But just to put it a little differently, with prepaid, you control how much money the carrier can take from you. With postpaid, you get a bill after they decided what you used. Postpaid usually implies a contract as well, but not always (T-Mobile for example).
If you put $30 on a prepaid account, it may turn out you didn't understand the terms, didn't understand the usage, etc... The carrier may burn through your $30 faster than you expected. But you will never be out more than the $30 (though you may have no minutes left for the rest of the month/etc).
If you have a postpaid account with $30/month service, it may turn out you didn't understand the terms, usage, etc. The carrier may just let you keep on going well past the services that come with your $30/month plan. And at the end of the month you get a phone bill for $150 of stuff you already used.